In the context of the mismatch between organ demand and supply, a statistic worth noting is that across the donor service areas in the United States, the average (median) percentage of eligible potential donors from whom no organs are recovered is 28.3% (29%). The socially suboptimal quantity and quality of recovered organs form the context of our study, which takes the perspective of the social planner that has an overall quality‐adjusted life‐year (QALY) improvement objective. We model the operational decisions of two key supply‐side entities in a cadaver organ donation value chain (ODVC)—the organ procurement organization (OPO), and the hospital (trauma center) where potential donors arrive. We consider the OPO’s effort level in seeking authorization for organ donation, the hospital’s effort level in identifying and referring potential donors to the OPO, and the hospital’s priority scheme for scheduling organ recovery and other procedures in its operating room (OR). We develop an analytical model to study the effects of contextual factors (including reimbursement rates for the hospital, shared OR capacity between organ recovery and other procedures, donor heterogeneity, and increments in QALYs for organ recipients and the hospital’s other patients), and the decisions of the OPO and the hospital, on their respective payoffs and on societal outcomes. Our analysis identifies possible misalignments in the objectives of the social planner, the OPO, and the hospital, and we recommend contracts that can help the ODVC achieve socially‐optimal QALY performance while ensuring that neither the OPO nor the hospital would be worse off.